R-Partity Breaking via Type II Seesaw, Gravitino Dark Matter and Positron Excess Shao-Long Chen University of Maryland Pheno 2009 Based on arXiv:0903.2562 in collaboration with R. N. Mohapatra, S. Nussinov and Yue Zhang Pheno 2009 – p.1/18
♦ Outline 1. Motivation; 2. R-parity violating via Type-II seesaw; 3. Cosmic electrons excess from Gravitino decay; 4. Summary. Pheno 2009 – p.2/18
PAMELA positrons excess -3 10 × 0.4 )) φ Donato 2001 (D, =500MV) 0.3 - (e φ 0.35 Simon 1998 (LBM, =500MV) φ )+ 0.2 φ Ptuskin 2006 (PD, =550MV) + (e 0.3 PAMELA φ ) / ( + 0.1 0.25 (e φ Positron fraction /p 0.2 p 0.15 0.1 0.02 0.05 PAMELA 0 0.01 2 1 10 100 10 1 10 Energy (GeV) kinetic energy (GeV) PAMELA: positron excess but no anti-proton in the energy range of 10 ∼ 100 GeV. PAMELA collaboration ArXiv:0810.4994, 0810.4995 Pheno 2009 – p.3/18
Fermi, HESS, ATIC electrons/positrons excess ) -1 sr -1 s ∆ E ± 15% -2 m 2 dN/dE (GeV 2 10 3 E ATIC PPB-BETS Kobayashi H.E.S.S. H.E.S.S. - low-energy analysis Systematic error Systematic error - low-energy analysis Broken power-law fit 2 3 10 10 Energy (GeV) ArXiv:0905.0025, 0905.0105 Pheno 2009 – p.4/18
Modified background ArXiv:0905.0636[astro-ph.HE] The black continuos line corresponds to the conventional model used in (Strong et al. 2004 ) and the red dashed and blue dot-dashed lines are obtained with modified injection indexes in order to fit Fermi-LAT CRE data. Pheno 2009 – p.5/18
Interpretation of the observations ♣ Astrophysical sources: Nearby pulsars, ... ♣ Dark matter: stable dark matter pair annihilation and decaying dark matter how to explain the lack of any excess in the hadrons? how does one get an adequate enough electron/positron production rate to explain the excess? dark matter pair annihilation: an additional enhancement ( ∼ 10 2 − 3 ) is ♦ required for the annihilation cross section required by relic density. (Sommerfeld enhancement, Breit-Wigner resonance, non-thermal relic density, or nearby clump dark matter, ...) dark matter decay: ∼ 10 26 sec lifetime. ♦ with Leptophilic channels, either by dynamics or kinematically. Pheno 2009 – p.6/18
Gravitino as the decaying dark matter with RPV. Due to the factor 1 /M P lanck suppression, gravitino has very long lifetime to be dark matter. Considering MSSM with RPV terms LLe c , QLd c , u c d c d c and LH u . ˜ G mainly decays to Zν, γν, W ± ℓ ∓ . ⇒ both leptons as well as hadrons in the final states of gravitino decay. If one kept only the LLe c term, then the predominant decay mode of the gravitino will only be to leptons. While the strength of the coupling λ required for keeping baryon asymmetry is too small ( λ < 10 − 7 ) [B. A. Campbell et al. (1991); H. Dreiner et al. (1993).] to explain neutrino masses via loop corrections. Pheno 2009 – p.7/18
We propose a new class of R-parity violating interactions that can arise in extensions of MSSM: ♦ explains small neutrino masses and mixings via the type II seesaw mechanism; ♦ keeps the baryon asymmetry of the universe untouched; ♦ able to explain the leptophilic nature of the PAMELA observations. Pheno 2009 – p.8/18
A well hidden in low energy processes RPV term extend MSSM by adding SU (2) L triplets ∆ , ¯ ∆ with Y = ± 2 . with the superpotential as: λ u Q T iτ 2 H u u c + λ d Q T iτ 2 H d d c + λ l L T iτ 2 H d e c + µH u H d W = ` ´ + fL T iτ 2 ∆ L + ǫ d H T u iτ 2 ¯ ∆ ¯ d iτ 2 ∆ H d + ǫ u H T ∆ H u + µ ∆ Tr ∆ ` ´ L T iτ 2 ∆ e + f A e L + ǫ dA H T d iτ 2 ∆ H d + ǫ uA H T u iτ 2 ¯ ∆ ¯ ∆ H u + b ∆ Tr ∆ + h.c. . ♣ add R-parity violating term: δW � R = a ∆ H d L. The associated soft breaking terms is: L � R = ρ � L ∆ H d + h . c . Pheno 2009 – p.9/18
Neutrino masse: through by type II seesaw after the triplet Higgs gets vev v T ∼ ǫ u,d v 2 wk /M S . m ν = 2 fv T � 0 . 1eV , then implies that if v T ≤ MeV ( ǫ u,d ≤ 10 − 5 ), f ≥ 10 − 7 . ν − � ∆ mixing gives contribution ∼ ( av wk ) 2 /M SUSY via a seesaw-like formula, but negligible compared to that from type II. LFV constraints on the couplings f , eg. µ → 3 e gives f 11 f 12 ≤ 10 − 6 . Pheno 2009 – p.10/18
♣ RPV induced mixing and Gravitino decay: The ∆ − � ℓ mixing: e ∆ ≃ ( ρ + aµ ) v wk U e . m 2 e − m 2 e ∆ Then the gravitino will decay through � G → ℓδ → ℓℓν . γν , � Wℓ , � These mixings between � Zν etc. are severely suppressed. 0 > 0 > 0 > <H d <H d <H d ~ ~ ~ − − l 0 l l ~ ~ ~ l − W − Z ~ ~ ~ 0 0 0 ˜ G → νδ 0 (3 ν ) when m ˜ ♣ monochromatic neutrino signatures: G > m δ . Pheno 2009 – p.11/18
Radiative stability the radiative correction to ǫ is safe due to the non-renormalization theorem of SUSY. for ǫ A , due to symmetry argument (lepton number and restored PQ symmetry by assigning charges to fields and spurion’s parameters see Arxiv:0903.2562 appendix). � ǫ A � 1 16 π 2 a 2 .f δ ∝ v wk So the smallness of ǫ A is stable under radiative corrections. the usual R-parity violating MSSM terms generated through radiative corrections Their strengths are, however, very weak and do not lead to any observable effects. E c H d Q H d H u H d H u L H u L L L H u H d − − D c L Pheno 2009 – p.12/18
Diffusion The transport equation x ) ∇ f e + ) + ∂ ∇ · ( K ( E, � ∂E ( b ( E, � x ) f e + ) + Q ( E, � x ) = 0 , f e + is the number density of positron per unit energy, K ( E, � x ) is the diffusion coefficient, b ( E ) ≈ 10 − 16 ( E/ 1 GeV ) 2 sec − 1 . b ( E, � x ) is the rate of energy loss dN e + ρ ( � x ) The source term Q ( E, � x ) = dE . m e G τ e G The solution of the transport equation at the Solar system can be expressed by the convention [Ibarra et al. 2008] Z E max 1 dE ′ G ( E, E ′ ) dN e + f e + ( E ) = dE ′ , m e G τ e 0 G The positron flux from gravitino decay can then be obtained from Z E max ( E ) = c c dE ′ G ( E, E ′ ) dN e + Φ prim 4 π f e + ( E ) = dE ′ . e + 4 πm e G τ e 0 G Pheno 2009 – p.13/18
Astrophysical background: We use the parametrizations obtained in [Baltz et al 1998, Moskalenko 1997] with the fluxes in units of (GeV − 1 cm − 2 sec − 1 sr − 1 ): 0 . 16 E − 1 . 1 Φ prim ( E ) = 1 + 11 E 0 . 9 + 3 . 2 E 2 . 15 , e − 0 . 7 E 0 . 7 Φ sec e − ( E ) = 1 + 110 E 1 . 5 + 600 E 2 . 9 + 580 E 4 . 2 , 4 . 5 E 0 . 7 Φ sec e + ( E ) = 1 + 650 E 2 . 3 + 1500 E 4 . 2 , where E is expressed in units of GeV. Pheno 2009 – p.14/18
To fit the PAMELA’s data, as an example, we take m e G = 350 GeV, m ∆ = 700 ℓ ∆ | = 2 . 5 × 10 − 8 , therefore the lifetime of gravitino is about 2 . 1 × 10 26 GeV, | fU e sec (for simplicity, degenerate neutrino mass hierarchy used). )) - (e )+ 0.1 + (e )/( + (e PAMELA Background Gravitino decay 0.01 1 10 100 Energy [GeV] Pheno 2009 – p.15/18
The fit after Fermi LAT data ] 2 GeV )) - (e -1 0.1 sr ) + -1 + (e sec ) / ( -2 100 dN/dE [m + (e 0.01 ATIC 3 PAMELA E FERMI background gravitino decay gravitino decay background 1E-3 10 10 100 1000 10 100 1000 Energy [GeV] Energy [GeV] G = 0 . 42 × 10 26 sec by taking the Here we use m ˜ G = 3 TeV, m δ = 2 . 9 TeV, τ ˜ neutrino mass normal hierarchy. (Triplet Higgs ∆ mainly decay to µ and τ ’s.) Pheno 2009 – p.16/18
Summary A new R parity violating scenario is proposed which related to the neutrino mass via type II seesaw. This provides a natural explain of small neutrino mass and the positron/electrons excess, but no excess in hadron. This class of R-parity breaking models remains very well hidden from low energy experimental probes. Pheno 2009 – p.17/18
backup slides Pheno 2009 – p.18/18
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